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Answer: Long about 877 shares.
## Explanation Using the binomial tree model to calculate delta: **Given**: - Short position in 2,000 call options - Current stock price (S) = $19 - Strike price (K) = $20 - Up state: S_u = $23.75 - Down state: S_d = $15.2 - Time to maturity = 1 month **Calculate option payoffs**: - Up state payoff: max(23.75 - 20, 0) = $3.75 - Down state payoff: max(15.2 - 20, 0) = $0 **Calculate delta**: \[ \Delta = \frac{C_u - C_d}{S_u - S_d} = \frac{3.75 - 0}{23.75 - 15.2} = \frac{3.75}{8.55} = 0.4386 \] **Hedge calculation**: - The trader is short 2,000 calls - Each call has delta of 0.4386 - Total delta position = -2,000 × 0.4386 = -877.2 To make the position delta neutral, the trader needs to offset this negative delta by buying shares: - Buy approximately 877 shares Therefore, the correct answer is **B: Long about 877 shares**.
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An option trader is currently holding short positions in 2,000 European call options that will all mature in one month. The current stock price is $19, while the strike price of those call options is $20. The trader is considering the delta hedging strategy based on a simple one-step binomial tree model. In the model setting, one month later, the stock price will be either $23.75 or $15.2. What should the trader do in order to make the position delta neutral?
A
Short about 877 shares.
B
Long about 877 shares.
C
Short about 1,111 shares.
D
Long about 1,111 shares.
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